Nywoek

A lot of countries don't stamp passports anymore. Every time you enter your passport is scanned and an electronic record is made (I 94)

you can get copies of your I-94s from the CBP website
https://i94.cbp.dhs.gov/I94/#/home
those would replace the passport stamps when it comes to evidence you've been to the US legally

Thanks guys, thats a valuable resource. 😃

Thank you! I submitted a request for one, and it will have some sort of special seal on it as well.

Always a yes

Thank you guys! I had to stop responding because the forum would not let me post. I was also up late so I actually had to wait 2 days, lol.
 
Update: I talked to the dad. He sees some benefits to this, so he might work with me. He even mentioned getting my kids passports, but he does not seem as motivated anymore, however I can do it my self with his permission. I was obviously never going to move the kids out of the country without his approval, I was just taking appropriate steps to make sure we knew what we were doing before filling him in. He is currently not very present in their lives, which I am trying to change, but I can only do so much, unfortunately.

We also talked to a caseworker/lawyer through these forums, and they said we can choose whether to just file normally or get passports for the kids. Even if they are technically american, since they arent in the system, we can just move on with this as normal. We just have to decide before a certain point in the process. However it would be easier for them to travel back and forth, so I will probably try to get them their paperwork.
 
We decided to go for the K1, might regret it, but my fiance is not a fan of the idea of an online wedding, and it would be hard to get all that in order before applying. We are currently pretty close to submitting the first part of our application. 😃 

I had to get them ESTAS last year when we visited for the summer.. then I just said they were Norwegian, so hopefully that wont come back to bite me later..

Oh, yeah I suppose you are right. But there is no tie to the US other than their dad being american, he never registered or filed taxes with them as dependents. He has been living in Norway for the past 15 years.
 
I would not mind getting them citizenship though, it is just a matter of their dad being somewhat difficult to deal with. But I need his permission to move out of the country anyway, due to Norwegian child laws, so I will have to do that anyway.
 
The current plan is to contact a lawyer that can advise us, but I would like to be prepared for that meeting, and also hear what other people might think we should do.
 
Thanks for responding. 😃

Some US citizens never been to the US. @Redro is right, the kids may get denied visas because citizens do not need visas to come to the US. If they're citizens, they'll need to get US passports. 

The issue is… if the kids are already American they don’t qualify for immigrant visas… or the K2.
So, have a chat with their dad. You can have a conversation around how they are rightfully US citizens and he is keeping them from going to his home country to understand/ learn about  their heritage… 

Oh, yeah I suppose you are right. But there is no tie to the US other than their dad being american, he never registered or filed taxes with them as dependents. He has been living in Norway for the past 15 years.
 
I would not mind getting them citizenship though, it is just a matter of their dad being somewhat difficult to deal with. But I need his permission to move out of the country anyway, due to Norwegian child laws, so I will have to do that anyway.
 
The current plan is to contact a lawyer that can advise us, but I would like to be prepared for that meeting, and also hear what other people might think we should do.
 
Thanks for responding. 😃

There might be issues IF you go through through the immigrant or K1 visa route for them, they are denied because they are US citizens… @Lemonslice might have more information about that… 
ETA you might have to have a difficult conversation with your ex to get your children their rightful US citizenship. 

That being said he has children with someone else and talked about going to the embassy to get them papers, potentially taking our kids to do the same on a later date. However at the time I do not think he was expecting we might move to the US.